Metamath Proof Explorer


Theorem 3bitr3g

Description: More general version of 3bitr3i . Useful for converting definitions in a formula. (Contributed by NM, 4-Jun-1995)

Ref Expression
Hypotheses 3bitr3g.1
|- ( ph -> ( ps <-> ch ) )
3bitr3g.2
|- ( ps <-> th )
3bitr3g.3
|- ( ch <-> ta )
Assertion 3bitr3g
|- ( ph -> ( th <-> ta ) )

Proof

Step Hyp Ref Expression
1 3bitr3g.1
 |-  ( ph -> ( ps <-> ch ) )
2 3bitr3g.2
 |-  ( ps <-> th )
3 3bitr3g.3
 |-  ( ch <-> ta )
4 2 1 bitr3id
 |-  ( ph -> ( th <-> ch ) )
5 4 3 syl6bb
 |-  ( ph -> ( th <-> ta ) )